Firstly, we recall that the bulk phase structures of \(Sp(4)\)  with and without (Wilson) fermions,
either in the fundamental or the antisymmetric representations,
have already been studied numerically on the lattice.
In the Yang-Mills case, the study of the standard plaquette action shows
that there is no bulk phase transition [1]}.
In the presence of fermionic matter, first order bulk phase transitions have been found,
for both choices of \((f)\)  and \((as)\)  (Wilson-Dirac) fermions [2]}, [3]}.
Interestingly, by comparing the results for the theory with
\(N_f=2\)  fundamental fermions, against the theory with \(n_f=3\)  antisymmetric fermions,
one finds that the weak coupling regime extends to different values of \(\beta \) ,
reaching to smaller values in the case of \((as)\)  fermions—the critical values of \(\beta \) , demarcating
strong and weak coupling regimes, are \(\beta _{\rm cr}^f\sim 6.7\)  [2]}
and \(\beta _{\rm cr}^{as}\sim 6.5\)  [3]}.
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